Dear keNt,
" 3. Some is also used when making requests and offers.
Can I have some milk? Would you like some tea? "
Ah, no thanks.
But " some " can be used with lots of questions besides requests and offers:

Are you taking some books with you?
Do you know some good examples?

I think it's easier just to say that " any " is used with negative statements, but that " some " can be used with positive statements and with questions.
Moreover, there's another meaning of " any " ( " it doesn't matter which " ) that can be used with positive statements: